I am successfully using child theming to make my modifications to the Display theme. However, if I want to have my own copy of style2.css, so my changes don’t change the original, I have two questions:

1. does my child style2.css file have to be in a similar directory structure inside my child theme folder, or can it just be in the same child theme directory as my version of style.css?

Not at all. So many people here are helping each other, it just seems like the thing to do.

I consider my suggestion above a hack, since I haven’t seen it described in Codex. It’s working well for me with the Newscast theme.

However, in an ideal world, I think the Child style.css file should be able to handle everything using @import url(style1.css); placed after the @import url(style.css). For example, it seems logical in a cascading world where the Child style.css should control everything that it would: 1. import and execute style.css, then 2. any mods to style.css, and then 3. import and execute style1.css, and then 4. any mods placed after that. However, the original header.php is executing style1.css (again?*) AFTER it processes the Child. *once during @import in the child and again because of the header <link> stmt.